Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

3.4K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
3.4K
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

125
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
125
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

648
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
648
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

135
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
135
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

865
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
865
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

1.5K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
1.5K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Effect of linaclotide combined with polyethylene glycol on bowel preparation before colonoscopy in patients with constipation.

Frontiers in medicine·2026
Same author

EP300 promotes hepatocellular carcinoma proliferation, migration and in vivo tumorigenicity revealed by integrated experimental and bioinformatic analyses.

Journal of translational medicine·2026
Same author

Atlas-Based Mapping of Traditional Chinese Medicine Effects on Tumor Microcirculation Regulation.

Immunity, inflammation and disease·2026
Same author

Arabidopsis XPD functions upstream of CDKA;1 to regulate stomatal development.

The New phytologist·2026
Same author

Value of albumin-bilirubin grade for 90-day mortality and long-term outcomes in patients with perihilar cholangiocarcinoma: a multicenter retrospective cohort study.

Therapeutic advances in medical oncology·2026
Same author

Biomolecule-tailored chiral nickel oxide nanozymes amplify autophagy-mediated tumor ablation via synergistic photodynamic-chemodynamic therapy.

Materials today. Bio·2026

Related Experiment Video

Updated: Sep 13, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.6K

A Lattice Boltzmann BGK Model with an Amending Function for Two-Dimensional Second-Order Nonlinear Partial

Xiaohua Bi1, Junbo Lei2, Demei Li2

  • 1School of Liberal Arts and Sciences, North China Institute of Aerospace Engineering, Langfang 065000, China.

Entropy (Basel, Switzerland)
|July 29, 2025
PubMed
Summary

This study introduces a novel lattice Boltzmann method (LBM) for solving nonlinear partial differential equations. The proposed mesoscopic model offers an efficient and stable approach for simulating complex nonlinear dynamics.

Keywords:
Chapman–Enskog expansionD2Q4 modellattice Boltzmann methodsecond-order nonlinear partial differential equation

More Related Videos

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
10:23

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

544
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.0K

Related Experiment Videos

Last Updated: Sep 13, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.6K
Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
10:23

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

544
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.0K

Area of Science:

  • Computational Physics
  • Applied Mathematics
  • Numerical Analysis

Background:

  • Nonlinear partial differential equations (PDEs) are fundamental in describing complex phenomena.
  • Existing numerical methods may face challenges with stability and efficiency for strongly nonlinear systems.
  • The lattice Boltzmann method (LBM) offers a promising alternative for fluid dynamics and beyond.

Purpose of the Study:

  • To develop a mesoscopic lattice Boltzmann method (LBM) based on the BGK model for solving 2D second-order nonlinear PDEs.
  • To incorporate an amending function for enhanced accuracy and stability.
  • To systematically investigate the numerical characteristics and evolution patterns of these nonlinear equations.

Main Methods:

  • A D2Q4 lattice model was employed within the LBM framework.
  • Kinetic moment constraints for equilibrium and correction distribution functions were derived.
  • Chapman-Enskog analysis was used to verify recovery of macroscopic equations in the continuous limit.
  • Numerical experiments with exact solutions were conducted to assess accuracy and stability.

Main Results:

  • The proposed LBM successfully simulates initial value problems of second-order nonlinear PDEs.
  • The model demonstrates efficiency and stability, even for strongly nonlinear cases.
  • Numerical experiments showed excellent agreement with exact solutions, confirming model accuracy.
  • The robustness of the model in capturing nonlinear dynamics was validated.

Conclusions:

  • The mesoscopic LBM with an amending function provides an effective and stable numerical framework for 2D second-order nonlinear PDEs.
  • The model is adaptable to various nonlinear systems, offering a versatile tool for scientific investigation.
  • This approach enhances the capability of LBM for tackling complex nonlinear phenomena.